Guitars and other stringed instruments are often amplified by attaching a passive magnetic pickup in close proximity to the vibrating metallic strings and connecting this pickup to an amplifier and speaker using a cable. The vibrating string changes the magnetic flux within the core of the pickup. This flux change induces a voltage change in the outer coils of the pickup, thus completing the translation of mechanical vibration to electrical signal. This signal is transmitted through the cable to the amplifier.
The cable connecting the pickup to the amplifier is typically between 5 and 30 feet in length to allow the musician adequate mobility while playing. For increased mobility, some musicians use wireless transmitters which allow substantially greater distances between the guitar and amplifier, however, the vast majority of musicians don't require the additional distance and prefer to use the less expensive cable connection.
In addition to the electrical requirements of a guitar cable, the guitar cable must have a combination of mechanical attributes. Guitar cables need to withstand tensile forces when extracting them from the jacks in guitars and amplifiers. Cables require adequate flexibility to not inhibit movement by the player and need to be robust enough to endure the random flexing exerted by players through constant movement. They also need to withstand the forces of coiling and uncoiling associated with storage when not in use.
Coaxial cable, where the signal is surrounded by a 360 degree metallic wire shield, is the most common connection between the electric guitar and the amplifier. The coaxial structure offers several advantages over other cable designs. The outer shield protects the low voltage signals traveling inside the cable's core from radio frequency interference (RFI) which is important since the guitar signal, along with any RFI noise, is significantly amplified prior to the speaker. The coax structure offers the minimum size for a shielded cable for a given capacitance. The round structure allows for maximum flexibility in all directions. This is important during use as well as when winding the cable up for storage.
Electrical models have been created for the circuit of a passive guitar pickup connected to an amplifier using a cable (see for example the Instruction Manual for the Lemme Pickup Analyzer). The circuit shown in FIG. 1 is modeled as a pickup, cable and amplifier. The cable, when used for audio frequencies at lengths up to 500 feet can be viewed as a series resistor, equivalent to the total resistance of the signal path, and a parallel capacitor, whose value equals the lumped capacitance of the signal path. The amplifier input circuit is very high impedance, typically 500,000 Ohms to 1,000,000 Ohms. Given the voltage divider circuit between the cable resistance and amplifier input resistance, the signal transmission of the circuit is relatively insensitive to cable resistance below 50-100 ohms. Instrument cables have resistance values well below this range.
The frequency response of the circuit is dependent on the interaction of the pickup inductance and cable capacitance. A resonant frequency is created where the reactance of the cable capacitance and pickup inductance are equivalent in amplitude. The resonant frequency of the circuit in FIG. 1 is calculated by:
      f    r    =      1          2      ⁢                          ⁢      π      ⁢              LC            Where L is the fixed pickup inductance and C is the lumped cable capacitance, which is determined by the cable design and length. The resonant frequency is inversely proportional to cable capacitance. As cable capacitance is decreased the resonant frequency is increased.
Using a Lemme Pickup Analyzer the response of a 2005 Fender American Series Stratocaster bridge pickup was measured in series with various lengths of cable to achieve desired capacitance values (see FIG. 2). The response curves were also simulated using SPICE software.
The circuit simulation along with measurements in FIG. 2 also show that the amplitude of the resonant frequency is decreased as the cable capacitance is decreased creating a flatter response in the guitar's midrange frequencies. The −3 dB roll-off frequency of the circuit response is also proportional to the cable capacitance. For a given pickup inductance, as the cable capacitance decreases, the −3 dB roll-off frequency will increase. This allows a wider range of audio frequencies to be transmitted and heard.
Shifts towards a wider range of audio frequencies above −3 dB, and a less emphasized resonant frequency, are readily perceived by guitar players as tonal shifts towards increased clarity and brightness. For a guitarist that would like this effect using an instrument with a passive magnetic pickup, it is necessary to minimize cable capacitance.
The coaxial cable capacitance (C) in picofarads per foot (pF/ft) is given by:
      Equation    ⁢                  ⁢    1    ⁢          :        ⁢                              ⁢                            ⁢    Coaxial    ⁢                  ⁢    Cable    ⁢                  ⁢    Capacitance        C    =                  7.36        ⁢                                  ⁢                  ɛ          r                            log        ⁡                  (                                    D              e                                      d              e                                )                                    Where:                    ∈r=Relative dielectric constant            De=Effective inner diameter of the outer shield            de=Effective outer diameter of the center conductor                        
The effective diameter is the electrical equivalent diameter of multiple conductor geometry. It takes into account the gaps between wires in specific constructions.
The effective diameters (De) of shields are calculated by:De=D, for a round tube or foil wrapDe=D+1.5dw, for a braided shieldDe=D+0.8dw, for a served shield                Where:        D=the geometrical outer diameter of an insulation component contacting the inner diameter of a shield construction        dw=geometrical diameter of shield component wire        
The effective diameters (de) of concentric stranded center conductors are calculated using:de=d, for a single wirede=2.84d, for n=7de=3.99d, for n=12de=4.90d, for n=19de=6.86d, for n=37                Where:        d=geometrical diameter of a center conductor component wire        n=number of component wires        
While there are several ways to reduce cable capacitance, each has a distinct disadvantage:                Reducing the relative dielectric constant of the material between the center conductor and shield: Several inexpensive materials, such as polyethylene, can have gas injected into them during processing to reduce the dielectric constant to approximately 1.5. To achieve dielectric constants below this requires more expensive processes and lower dielectric materials such as fluoropolymers.        Increasing the effective inner diameter of the outer shield: This option is bounded by the cost of adding material and the practical limits of the cable diameter that will fit into connector sizes.        Reducing the effective outer diameter of the center conductor: Typical commercially available cables use 18-22 AWG copper center conductors. This range of wire gage represents conductors with an outer diameter ranging from approximately 0.0500 to 0.0253 inches respectively. The conductor can be a solid conductor or multiple conductors to achieve the proper size. Some multiple conductor examples can be found down to 26 AWG copper, which has an outer diameter of approximately 0.0200 inches. Component wire diameters (d) in these multiple configurations can be found down to 0.002 inches. To reduce the effective diameter of the center conductor, the component wire (d) and number of strands should be decreased as shown under Equation 1. As the component wire diameter (d) and number of strands is decreased, the total cross-sectional area of the center conductor wires is decreased. A smaller cross-sectional area results in a lower tensile force at failure for a given material. This compromises both flex life and tensile strength of the cable.What is needed to improve signal fidelity of instrument cables is a cable that has low capacitance while maintaining strength, durability, connector compatibility, and cost effectiveness.        